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# Algebra 2 help

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Problem: If $$log{}_{2}x=7$$,find $$log{}_{8}x.$$

I am not allowed to use a calculator on this problem.

These are steps I have so far:

27=x

x=128

log8128=y

8y=128

y=$$\frac{log 128}{log 8}$$

And this is where I am stuck. I have to use a calculator for this part. Is there a way to solve this without using a calculator?

Thanks.

Jun 19, 2021

#1
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So far, you're doing really well..

After $$y = {log128\over log8}$$  you don't really need a calculator to solve this

We can write this as

$$y= {log 2^7\over log 2^3}$$  right?

then $$y= {7log2\over 3log2}$$

⇒$$y={7\over 3}$$

$${log}_{8}x = {7\over 3}$$

Hope you got it :)

Jun 19, 2021
edited by amygdaleon305  Jun 19, 2021
#2
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Oh yea you can write it like that then use the log rules and division. Thanks for the help!

LightningSidd  Jun 19, 2021